After the discovery of the 125Higgs boson (\(\) ) [1]}, [2]},
searches for additional Higgs bosons, based on predictions beyond the standard model (SM),
constitute an important part of the scientific program at the CERN Large Hadron Collider (LHC).
The present analysis examines theoretical models that contain two Higgs doublets
and an additional complex singlet Higgs field (denoted hereafter as 2HD+1S), that does not couple
at tree level to fermions or gauge bosons and interacts only with itself and the
Higgs doublets [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
In CP conserving models, which are considered in this Letter, the Higgs sector features seven
physical states, namely three CP-even, two CP-odd, and two charged bosons, where one of the CP-even states corresponds to the H.
This kind of Higgs sector is realized, for example, in next-to-minimal
supersymmetric models that solve the so-called \(\mu \)  problem of
the minimal supersymmetric extension of the SM [11]}.
A large set of the 2HD+1S models is allowed by
measurements and constraints set by searches
for additional Higgs bosons and supersymmetric particles [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
